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Properties

Label 5.3.6.1.2
Class number $1$
Dimension $5$
Determinant $3$
Level $6$

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Lattice Invariants

Dimension:$5$
Determinant:$3$
Level:$6$
Density:$0.0949703126294009395263498491746\dots$
Group order:$576$
Hermite number:$0.802741561760230682095169538063\dots$
Minimal vector length:$1$
Kissing number:$6$
Normalized minimal vectors: $(1, 0, 0, 0, 0)$, $(0, 1, 0, 0, 0)$, $(0, 0, 1, 0, 0)$
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Theta Series

\(1 \) \(\mathstrut +\mathstrut 6 q \) \(\mathstrut +\mathstrut 18 q^{2} \) \(\mathstrut +\mathstrut 44 q^{3} \) \(\mathstrut +\mathstrut 78 q^{4} \) \(\mathstrut +\mathstrut 72 q^{5} \) \(\mathstrut +\mathstrut 66 q^{6} \) \(\mathstrut +\mathstrut 180 q^{7} \) \(\mathstrut +\mathstrut 234 q^{8} \) \(\mathstrut +\mathstrut 114 q^{9} \) \(\mathstrut +\mathstrut 204 q^{10} \) \(\mathstrut +\mathstrut 396 q^{11} \) \(\mathstrut +\mathstrut 332 q^{12} \) \(\mathstrut +\mathstrut 312 q^{13} \) \(\mathstrut +\mathstrut 324 q^{14} \) \(\mathstrut +\mathstrut 396 q^{15} \) \(\mathstrut +\mathstrut 654 q^{16} \) \(\mathstrut +\mathstrut 468 q^{17} \) \(\mathstrut +\mathstrut 342 q^{18} \) \(\mathstrut +\mathstrut 924 q^{19} \) \(\mathstrut +\mathstrut 936 q^{20} \) \(\mathstrut +\mathstrut O(q^{21}) \)

Gram Matrix

$\left(\begin{array}{rrrrr} 1 & 0 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 2 & 1 \\ 0 & 0 & 0 & 1 & 2 \end{array}\right)$

Genus Structure

Genus representatives:
Class number:$1$
 
$\left(\begin{array}{rrrrr} 1 & 0 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 2 & 1 \\ 0 & 0 & 0 & 1 & 2 \end{array}\right)$
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